We've all heard of ageing rock stars making a comeback, but what's with the Muppets? Kermit the frog, who first took shape in an American college art class in the mid-1950s, is back on the chatshow circuit. The latest Muppet movie has garnered five-star reviews on both sides of the Atlantic and an Oscar nomination for best song. And yet Kermit is still wearing that jagged, green felt collar that looks like something cut out by a kid in a craft workshop.

I suspect that the current success of the Muppets is largely down to nostalgia. Those of us who grew up on Sesame Street and the Muppet Show will happily accompany our offspring to the cinema where we can chuckle at the postmodern, satirical script. But don't you also love the fact that the Muppets remain so touchingly unsophisticated and low-tech? Disney may have bought them up, but the Muppets represent a triumph of felt and foam over computer-generated imagery.

The art of puppetry more generally is enjoying something of a renaissance thanks to the National Theatre's huge success with War Horse. The stage show – which is now a worldwide hit – features lifesize equine puppets made from cane, plywood and mesh, which are manipulated on stage by three actors.

I cried at the National Theatre, and yet I can't face the maudlin sentimentality of the film. Puppets allow us to fill in the gaps with our imagination instead of having our emotions manipulated by sunsets and doom-laden orchestral music. Call me a luddite, but just as I like getting my vegetables delivered in a box direct from a farm in Devon, I love knowing that the puppets in War Horse are handmade in a workshop in Cape Town. It's also about scale. I like to know small enterprises can still make it big with a bit of wood, glue and string.

Adrian Kohler and Basil Jones, the South African founders of the Handspring Puppet Company behind War Horse, believe puppets reinvent the everyday in a powerful way. "It's the small things we do. If a puppet passes a cup to another puppet, it has a poignancy, an epic quality which is hard for an actor to find," says Kohler. "It's almost like you are seeing it with a child's eyes. It's a praise poem to the quotidian."

We used to think of puppets as entertainment for kids, but that's no longer the case. Even the Royal Shakespeare Company is using them. Two recent productions, The Tempest and a staging of Shakespeare's epic poem Venus and Adonis, have been collaborations with London's Little Angel puppet theatre.

The Little Angel – founded by John and Lyndie Wright 50 years ago – still makes its puppets on site. Walking into their workshop is like stumbling into the opening scene of Pinocchio. There are people sitting on stools carving small heads out of wood. The craftsmanship is magical. The Venus puppet used in the RSC production was made from the softest calf leather with foam inside so she could sink erotically into the arms of the hard-wooden Adonis.

The cottage next door to the Little Angel is where the award-winning director of Atonement, Joe Wright, grew up helping his parents in the workshop after school. The nostalgia of that childhood will be evident in Wright's upcoming adaptation of Tolstoy's Anna Karenina, which will have puppets as well as Keira Knightley.

And there will be puppets performing during this summer's Olympic festivities. This comforts me in the same way Kermit's little felt collar does. Not just because the Olympic Games and puppetry are traditions dating back to ancient times. But because they're spectacles created on a human scale, not by some unseen digital manipulation.